Which of the following numbers is a multiple of 9? ${63,78,88,106,109}$
Explanation: The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $63 \div 9 = 7$ $78 \div 9 = 8\text{ R }6$ $88 \div 9 = 9\text{ R }7$ $106 \div 9 = 11\text{ R }7$ $109 \div 9 = 12\text{ R }1$ The only answer choice that leaves no remainder after the division is $63$ $ 7$ $9$ $63$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $63$ $63 = 3\times3\times7 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $63$. We can say that $63$ is divisible by $9$.